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 A279544 Number of length n inversion sequences avoiding the patterns 000, 010, 110, 120, and 210. 2
 1, 1, 2, 4, 10, 26, 73, 214, 651, 2040, 6549, 21453, 71485, 241702, 827603, 2865087, 10014927, 35307628, 125427569, 448616693, 1614432373, 5842129120, 21247505098, 77631329535, 284832049361, 1049092809734, 3877749157355, 14380314221305, 53490244751332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 000, 010, 110, 120, and 210. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..600 Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016. FORMULA a(n) ~ c * 4^n / n^(3/2), where c = 0.0549097036253448014962069269284638611865763295943683310517... - Vaclav Kotesovec, Oct 07 2021 EXAMPLE For n=3, the inversion sequences are 001, 002, 011, 012. MAPLE b:= proc(n, i, m) option remember; `if`(i=0, 1, add( b(n-min(m, j), i-1, abs(m-j)), j=1..n-i+1)) end: a:= n-> b(n\$2, 0): seq(a(n), n=0..30); # Alois P. Heinz, Dec 15 2016 MATHEMATICA b[n_, i_, m_] := b[n, i, m] = If[i == 0, 1, Sum[b[n - Min[m, j], i - 1, Abs[m - j]], {j, 1, n - i + 1}]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 10 2017, after Alois P. Heinz *) CROSSREFS Cf. A000085, A263777, A263778, A263779, A263780. Sequence in context: A210043 A049130 A101488 * A245898 A230662 A351642 Adjacent sequences: A279541 A279542 A279543 * A279545 A279546 A279547 KEYWORD nonn AUTHOR Megan A. Martinez, Dec 14 2016 EXTENSIONS a(10)-a(28) from Alois P. Heinz, Dec 14 2016 STATUS approved

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Last modified April 23 16:40 EDT 2024. Contains 371916 sequences. (Running on oeis4.)